A New Perspective on Tree Adjoining Grammar - University of Delaware

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(3) Whati do you think Mary saw ti? The constrained nature of the adjoining operation (operating on a tree-to-tree basis) also has desirable results with regard to ...

Monotonic C-Command: A New Perspective on Tree Adjoining Grammar Robert Frank ([email protected]) Dept. of Cognitive Science, Johns Hopkins University

Seth Kulick ([email protected]) Institute for Research in Cognitive Science, University of Pennsylvania

K. Vijay-Shanker ([email protected]) Dept. of Computer and Information Sciences, University of Delaware Abstract. In this paper we argue for a reconceptualization of the Tree Adjoining Grammar (TAG) formalism, in which the elementary structures are collections of c-command relations, and the combinatory operation is substitution. We show how the formalism we sketch resolves a number of problems for TAG that have been identified in the literature. Additionally, we demonstrate that our proposal is preferable to other previously proposed extensions to TAG, for example D-tree grammars (Rambow et al., 1995), in that it preserves many of the linguistically desirable aspects of TAG’s restrictiveness, specifically concerning the derivation of locality constraints on unbounded dependencies. Keywords: C-Command, Long-Distance Dependencies, Tree Adjoining Grammar

1. Introduction The Tree Adjoining Grammar (TAG) formalism has a number of properties that make it attractive for use in natural language analysis. Specifically, the use of the adjoining operation allows the specification of grammatical constraints to be separated from the recursive processes in the grammar. This leads to an elegant analysis of extraction in TAG which allows the specification of co-occurrence constraints to remain stated within the local domains determined by the elementary trees (Kroch and Joshi, 1985; Frank, 1992). Over the last 15 years, however, it has been pointed out a number of times that there exist linguistic phenomena that pose problems for this elegant analysis. This has led to a variety of proposed extensions to the basic TAG formalism. The most successful of these extensions with regard to capturing the broadest range of problematic cases have, unfortunately, also extended the formal power of TAG, so much so that grammatical constraints like Subjacency, that had been found to be derivable from general c 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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Frank, Kulick and Vijay-Shanker X X

Y Y

Y Y Y

(A)

(B)

(C)

Figure 1. Adjoining in TAG

architectural properties of the TAG adjoining operation (Kroch, 1987), must now be explicitly stated in the extended formal systems. In this paper we argue for a reconceptualization of the TAG formalism, in which the elementary structures are collections of c-command relations and the combinatory operation is substitution, thus refining and expanding upon a proposal made by Frank and Vijay-Shanker (1998b). This extension turns out to be sufficiently powerful to capture previously problematic cases, though it preserves many of the linguistically desirable aspects of TAG’s restrictiveness. In section 2 we present a brief overview of TAG, in section 3 we discuss a couple of the empirical problems for the TAG analysis of extraction, and in section 4 we review a pair of proposed solutions. Section 5 presents the outline of our proposal, and in section 6 we illustrate how it is able to retain the linguistically relevant restrictiveness of the original TAG derivational system.

2. TAG and Extraction The separation of recursive processes in TAG is accomplished by localizing the grammatical constraints within small pieces of phrase structure, called elementary trees, which are combined using the adjoining operation. The adjoining operation operates by splitting a tree at one node, which we will call the adjoining site. In the resulting structure, the subtrees above and below the adjoining site are separated by, and connected with, the auxiliary tree used in the composition, as shown in Figure 1. Trees which can be adjoined into another tree are auxiliary trees, and have a foot node along the frontier which is of the same category as the root node. As illustrated below, recursive structures are treated as auxiliary trees, which adjoin in to produce non-local dependencies. (In addition to adjoining, tree substitution is also used as a tree composition operation in TAG.) TAG is a formal system that combines elementary trees, but it is not a linguistic theory and imposes no constraints upon the nature of

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3

Monotonic C-Command: A New Perspective on TAG

(a)

(b)

IP

HH

H  HH 0

Gabriel

I

I

DPi

I0 VP

H  H0

HH

V

I

VP

to

HH 0

ti

I

seems

V

HH V

DP

eat

gnocchi

Figure 2. Elementary trees for subject to subject raising

these elementary trees. However, it does enforce a particular working hypothesis for all linguistic work in TAG, namely that the substantive theory of syntax must be stated over the bounded local domains of the elementary trees. We follow here the characterization of the elementary trees proposed by Frank (1992), in which the crucial point is that an elementary tree is built around some lexical predicate and includes all of the syntactic structure necessary for the realization of all of its semantic arguments, its so-called extended projection (Grimshaw, 1991). (1)

Condition on Elementary Tree Minimality (CETM): Every elementary tree consists of the extended projection of a single lexical head

Under the CETM, the building blocks of TAG derivations, the elementary trees, are larger than individual lexical items or individual phrase structure rules familiar from other formalisms. Rather, they are themselves phrase structure trees. This extended domain of locality of TAG allows the expression of lexically imposed constraints to be separated from the recursive processes involved in the construction of complex phrase markers and creation of long-distance dependencies, as in wh-movement. A TAG analysis of the subject raising construction (Kroch and Joshi, 1985; Frank, 1992) provides a clear demonstration of how the adjoining operation can be used to separate local dependencies from recursive grammatical processes. Consider the raising sentence in (2). (2)

Gabriel seems to eat gnocchi

The tree headed by eat, given in Figure 2(a), is its IP extended projection. Note that the tree for seems, in Figure 2(b), lacks a position for the matrix subject Gabriel, since seems does not select for a subject.

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Frank, Kulick and Vijay-Shanker

IP



HH

DPi Gabriel

H0 I



H  H

I

H VP



H  H

seems

H0 I

V

HH I

VP

to

HH 0

ti

V

HH V

DP

eat

gnocchi

Figure 3. Result of TAG raising derivation

The recursive structure of auxiliary trees, together with the lack of a [Spec, IP] position, requires that seems takes an I 0 complement in the tree in Figure 2(b). This auxiliary tree adjoins at the I 0 node of the eat tree to form the tree in Figure 3. A distinctive feature of the TAG analysis is that there is no “movement” from one clause to another. Whatever movement there may be (e.g., that of the subject from its VP-internal position to [Spec, IP]) is internal to an elementary tree, and the appearance of inter-clausal movement results by segments of a tree getting stretched away from the rest of the tree, as illustrated by the Gabriel portion of the tree in Figure 2(a) being separated from the rest of its elementary tree in the resulting structure in Figure 3. The analysis of wh-movement, as in (3), is similar. The auxiliary tree given in Figure 4(b) is adjoined into the initial tree in (a) (with what moved to [Spec, CP]) at the C0 node, thus stretching what away from that Mary saw. (3)

Whati do you think Mary saw ti ?

The constrained nature of the adjoining operation (operating on a tree-to-tree basis) also has desirable results with regard to certain well-known constraints on the locality of various types of inter-clausal movements. In the context of the raising construction, it has been observed that sentences like (4), so-called “super raising”, are impossible, since Gabriel has moved “too far” past one intervening subject position to the next higher one. Strikingly, nothing needs to be added to the TAG analysis presented above to derive this result. (4)

* Gabriel seems it is likely to eat gnocchi.

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Monotonic C-Command: A New Perspective on TAG

(a)

(b)

CP

C0

H   HH 0

Whati

H  HH C

C

H  HH C

IP

H  HH

dok

IP

H  H 0

H  H

you

I

DPj

I0

DP I

HH

Mary

I

VP

H  H0

V

tk

VP

HH 0

tj

C

think

V

H  H V

ti

saw Figure 4. Elementary trees for long-distance wh-movement

(a)

(b)

I0

HH I

IP

H  H

VP

H  H V seems

I0

DP IP

it

HH I is

AP

H  H0

A

I

likely Figure 5. Elementary trees that can’t produce super raising

Since neither of the trees in Figure 5 have identical foot and root nodes, neither are TAG auxiliary trees. However, under a different conception of tree composition operations, it might be possible to combine together the trees from Figure 5 to form an I0 recursive tree for seems it is likely that could then adjoin into the tree in Figure 2(a), thereby deriving the super-raising case. However, this derivation is impossible in TAG since it cannot be expressed by a well-formed derivation tree. Without going into the technical details, auxiliary trees must be “born”, not “made” (see Frank (1992) for a discussion of this case). Other cases of locality constraints have been similarly derived (Kroch, 1987; Kroch, 1989), providing strong support for the role of adjoining in establishing long-distance dependencies.

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Frank, Kulick and Vijay-Shanker

C0

HH  H C

IP



HH

DP Gabriel

H0 I

HH VP

I to

HH V

DP

eat

gnocchi

Figure 6. Infinitival elementary tree

3. Two Problems for TAG As attractive as the account of long-distance dependencies just sketched is, a number of serious problems for this account have been identified in the literature. In this section, we focus on two such problems. The first of these concerns the phenomenon of modifier extraposition, as seen in (5). (5)

A student walked in who Alice had asked about.

Here, the relative clause who Alice had asked about is interpreted as modifying the subject, in spite of its apparent attachment to the right of the clause. Even if we assume that the noun phrase a student and its modifying relative are generated within a single elementary tree, there are no linguistically coherent structures that could be assigned to this elementary tree and the one headed by walked that could derive (5) through an application of adjoining. A second problem arises from the interaction of the raising construction, discussed earlier, and subject-auxiliary inversion, as in (6). (6)

Does Gabriel seem to eat gnocchi?

The elementary tree for the eat clause in this example is shown in Figure 6. By the CETM, does should originate in the same elementary tree as seems. However, since the raising auxiliary adjoins to the I 0 node, there is no way to include the auxiliary verb does within the seems tree so that it ends up in a position preceding the subject DP in the final sentence. That is, adjoining at I0 “stretches” Gabriel away from to eat gnocchi, without allowing the type of “interleaving” necessary to derive (6). This problem arises in an even more severe form when there is simultaneously wh-extraction of the PP experiencer complement to the raising verb:

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Monotonic C-Command: A New Perspective on TAG

DP

IP

H

H  HH

DP

ti

 IP

7

H CPi



PPP P 

PP

who Alice had asked about Figure 7. Multi-component tree set for extraposition from subject position

(7)

To whomi does Gabriel seem ti to eat gnocchi?

Since to whom is an argument of seem, they should be in the same tree. Here, not only do we have the previous problem of do-support, but to whom should be in the same elementary tree as seem as well, and the adjoining operation will not allow to whom and does to be distributed properly to derive (7). A number of other problems for TAG have also been discussed in the literature, such as clitic climbing (Bleam, 1994; Kulick, 1997), long distance-scrambling (Becker et al., 1991; Rambow, 1994), and raising in VSO languages (Harley and Kulick, 1998). While we focus on the cases just discussed, it is our contention that there is a close relationship between all of these problematic cases (see Kulick (1998) for a detailed discussion of this point), and that the analysis we propose here will be adaptable to those other cases. 4. Extensions to TAG To approach the types of problems discussed in the previous section, a variety of extensions to TAG have been proposed. The first of these is tree-local multi-component TAG (TL-MCTAG), in which the basic structures are no longer single trees, but instead sets of trees. 1 All the elements of the tree sets are required to adjoin (or substitute) at distinct nodes of a single (underived) elementary tree. Kroch and Joshi (1987) propose using this approach to handle the extraposition problem illustrated in example (5). They suggest that the tree set in Figure 7, containing an adjoined trace and the relative clause modifier, would be simultaneously adjoined respectively to the subject and the IP node of an elementary tree corresponding to the simple clause a student walked in, thereby deriving (5). As Kroch and Joshi note, extraposition may also take place from object noun phrases. (8)

I met the student yesterday who Alice had asked about.

Kroch and Joshi provide evidence that the landing site for extraposition from object is structurally lower than that for extraposition from

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Frank, Kulick and Vijay-Shanker

(a)

(b)

CP



H  H

DPi

C



H

C

C

what

H H 

do

C

H  HH C

IP

HH I

DP you

IP

H

HH I

VP

H  H

H  H

V

I

DP

HH Mary

I

C

think

VP

H  H V

ti

saw Figure 8. DTG elementary trees for long-distance wh-movement

subject.2 To account for this difference, they suggest that examples like (8) must be generated using a slightly different tree set from that in Figure 7, one in which the auxiliary tree containing the relative clause adjoins to VP rather than IP. The existence of both tree sets in the grammar now raises the spectre of overgeneration however: we must now prevent the use of the object tree set in cases of subject extraposition, improperly adjoining the trace to the subject and the relative clause to the VP. Kroch and Joshi draw from the TAG literature on multi-component sets and suggest utilizing a “dominance” link between the foot of one of the components of the set, in their case the relative clause component, and the root of the other, the trace component. The effect of these dominance links is to restrict adjunction of the two members of multi-component set so that the dominance relation specified between them is maintained throughout the derivation. The presence of such a dominance link will therefore allow the adjunction of the set in (7) to the subject and IP as well as the adjunction of the VP-adjoined variant to the object and VP, but will not allow the adjunction of the VP-adjoined form to the subject and VP, as the foot of the relative auxiliary will not dominate the root of the DP subject adjoined trace. The idea of incorporating dominance into a TAG-like system is taken considerably further in D-tree grammars (DTG) (Rambow et al., 1995), which builds upon earlier work by Vijay-Shanker (1992). DTG recharacterizes the notion of a TAG derivation as the monotonic growth of dominance relations that characterize the structures being composed. The proposal in Vijay-Shanker (1992) rests crucially on the assumption

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Monotonic C-Command: A New Perspective on TAG

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that the elementary trees are characterized in terms of a domination relation among nodes, and that each potential adjoining site is represented by two nodes standing in a domination relation. Under this proposal, the derivation of (3) uses the structures in Figure 8 to derive the long-distance wh-movement. To accomplish the analog of adjoining in this system, the root and foot nodes of the tree depicted in Figure 8(b) are identified with the two C 0 nodes standing in a domination relation in Figure 8(a) (represented by the dotted line). This domination relation still holds after adjoining, as do all the other domination relations stated in defining the trees in Figure 8. (In sentences in which there is no adjoining at the C0 node, e.g., I wonder what Mary saw, these C0 nodes could collapse, preserving domination under the assumption that it is a reflexive relation.) DTG builds upon this idea by using tree sets related by domination links as the elementary components of the system, and adjoining is eliminated in favor of a new operation, subsertion, that allows components of two structures to combine by substitution, with the other components interleaving with each other. This approach is able to handle many of the problems that have been pointed out for TAG, including a number that are beyond the reach of TL-MCTAG (but see Kulick (1998)). Yet, while DTG retains the crucial TAG notion of an extended domain of locality, it abandons the TAG derivational constraints on how trees may interact. Thus, DTG analogs of the trees in Figure 5 can be used to derive the the super-raising violation, which, as discussed earlier, is ruled out by the character of TAG derivations. DTG specifies a method of stating constraints on a derivation which can be used to prohibit this derivation. 3 Both TL-MCTAG and DTG make crucial use of the dominance relation in extending the expressive power of TAG. However, this structural relation is not always appropriate for characterizing the relation among the various pieces of an elementary structure. Recall the raising/subject-auxiliary inversion example in (6). Frank (1992) proposed utilizing the TL-MCTAG approach to resolve this problem, using the tree set in Figure 9. The derivation proceeds by adjoining the (b) tree from this set into the elementary tree in Figure 6 at the I 0 node, while at the same time substituting the (a) tree from the set into the C node of the same tree. One disadvantage of this approach is that it requires that the inversion of does is represented rather differently here than in cases in which plain TAG suffices, as in the case of whmovement (see Figure 4), in which movement of the auxiliary can be simply represented in a single tree. A second disadvantage, and the one pertinent to our current concerns, stems from the fact that there is no dominance relation between the two components of the multi-

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Frank, Kulick and Vijay-Shanker

(a)

(b)

Ci

I0

HH

does

I

VP

H  H0 I

V

ti

seem Figure 9. Multi-component tree set for raising with inversion

(a)

(b)

I

VP

H  H

HH  H

Clitic loi

I

PRO



V0

DP

IP

HH I0

DPk

HH V

H

ti

mangiare

Gabriel

H  HH I

VP

vuolej

HH 0

tk

V

H  H V

VP

tj Figure 10. Multi-component elementary trees for clitic climbing and the derived structure

component tree set in Figure 9, i.e., between the fronted auxiliary verb that is substituted into the C position and the root of the I 0 auxiliary tree.4,5 Clitic climbing (Bleam, 1994) provides another example of a construction in which dominance relations do not provide the right descriptive vocabulary for characterizing relations among members of an elementary structure in a TAG like system. In this construction, illustrated in (9) for Italian, the pronominal object of an embedded verb appears attached to a higher verb. (9)

Gabriel lo vuole mangiare Gabriel it wants eat-inf ‘Gabriel wants to eat it.’

The most natural syntactic analysis of the tight morphological relationship between the “climbed” clitic and the matrix verb is one in which the clitic is directly adjoined to this verb. Since this clitic is an argument of the embedded verb, it must be generated in the same elementary tree set, as in Figure 10(a). The two halves of Figure 10(a) are adjoined and substituted into the elementary tree headed by mangiare, depicted in Figure 10(b). Once again, there is no domination relationship between the two halves of this multi-component tree set, in this case between the

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Monotonic C-Command: A New Perspective on TAG

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I foot node of clitic-hosting structure and the VP root node that is projected from the verb. Thus, some other mechanism must be exploited to force the clitic to adjoin in the appropriate context. 6 5. TAG Derivation as Monotonic C-Command As we have just seen, the dominance relation that is crucially exploited in TL-MCTAG and DTG is not sufficiently expressive to capture the full range of linguistic phenomena. Furthermore, even in cases where dominance does suffice, it is often far from clear what general grammatical principle motivates the statement of the requisite dominance relations. For example, for the structure in (8a) what is crucial grammatically is not a statement about duplicate C 0 nodes standing in a domination relation, but rather that the moved element what must stand in a different structural relation with its trace, that of c-command, both in the the elementary tree and throughout the derivation. Similarly, in the cases of extraposition and clitic climbing, the relevant relation between the extraposed relative and clitic respectively and their traces is that of c-command. Instead of compiling out the crucially important c-command relations into statements about domination, we suggest, following Frank and Vijay-Shanker (1998b), that the centrality of c-command be taken seriously and propose that c-command as opposed to domination be used in extending TAG. It turns out that given how adjoining and subsertion have been defined and the manner in which domination statements have been utilized in TL-MCTAG and DTG, this c-command relation will always be preserved during a derivation. Consequently, Frank and Vijay-Shanker (1998b) propose that this preservation of c-command is the defining property of the adjoining operation, and not a residual effect of the specific choice of dominance relations. Following the line taken in DTG, this leads to a view in which TAG elementary structures are defined by their c-command relations, and where TAG derivations constitute monotonic additions to a set of c-command relations. That is, instead of viewing TAG structures being defined in terms of domination relations, we consider any domination relations that will be preserved to arise or be inferred from the c-command relations used in defining TAG structures. 5.1. Elementary trees as c-command relations In characterizing TAG elementary trees, we make use of independently motivated assumptions concerning the c-command relations that exist among structural elements. Thus, we assume that the c-command

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Frank, Kulick and Vijay-Shanker

(a)

(b)

CP

H  HH what



H  HH C

do

IP



H  H

Cj

C

DPi

C0

H

DP

H

HH Mary

IP



I

ti

H0 I

 H H I tj

VP

H  H V

H  H

DP you

I

H

VP

H  H0

V

C

think

saw Figure 11. C-command-based elementary trees for long-distance wh-movement

relations within elementary trees will be determined by (at least) the following principles (cf. the definitions in Kayne (1994)): (10)

a. b. c. d.

A A A A

moved element c-commands its trace. head and its complement c-command one another. modifier c-commands the phrase it modifies. specifier c-commands the phrase to which it attaches.

Following these principles leads us to the structure in Figure 11(a) corresponding to the elementary tree in Figure 8(a) (where arrows indicate c-command relations).7 There are two crucial c-command relations to observe in this structure: the first between the fronted wh-phrase and its trace, and the second between the wh-phrase and the C 0 node, which serves as the target of movement within the elementary tree. The structure in Figure 11(b) is the c-command analog of the one in Figure 8(b), Let us suppose that derivations proceed as monotonic combinations of structures like this one defined in terms of c-command. This means that we can perform an operation analogous to adjoining, inserting the tree from FIgure 11(b) between the fronted wh-element and the C0 of Figure 11(a), by identifying this C 0 with the foot node of the auxiliary structure. In the structure that results, all of the c-command relations stated in the elementary trees are preserved, most notably those between the fronted wh-element and both the C 0 and its trace. From this perspective, we can now understand why it was necessary in the framework of Vijay-Shanker (1992) to posit a domination relation between the two C0 nodes in the structure in Figure 8(a): as an indirect representation of (at least) the principle requiring that moved elements c-command their traces.

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Monotonic C-Command: A New Perspective on TAG

(a)

(b)

NP

HH AP

P  P green

NP

13

DP

H  H D

NP

the

N idea

Figure 12. C-command-based elementary trees for adjectival modification

5.2. Deriving Constraints on Adjoining This proposal allows us to explain many previously stipulated properties of TAG elementary trees and constraints on the adjoining operation. Kroch (1989) and Schabes and Shieber (1994) noted structural differences between two classes of auxiliary trees: complement auxiliary trees on the one hand and modifier or athematic auxiliaries on the other. Modifier auxiliaries have the distinctive property that their foot node is the sister of a modifying phrase and is the daughter of the root node. Following the principles in (10), it follows that a modifier c-commands the XP phrase it modifies, though not vice-versa. The structure in Figure 12(a) is the c-command representation of a modifier auxiliary tree. The green AP node c-commands the NP it adjoins to, and so if the adjoining site is the NP node of Figure 12(b), the adjoining will form the green idea. The foot node of a complement auxiliary tree, in contrast, must be the sister of the head of which it is a complement. Thus, this foot node will both c-command and be c-commanded by its sister node. The structure from Figure 8(b) is a complement auxiliary tree, and its c-command analog in Figure 11 shows the mutual c-command relation between the V node think and the C0 foot node. It has sometimes been stipulated that adjoining of complement auxiliaries is blocked at the foot node of complement auxiliary trees. As just noted, since the foot of a complement auxiliary is a complement, this node c-commands the lexical head of the complement auxiliary tree. Adjoining to this foot node by another complement auxiliary tree will have the effect of lowering it, so that it no longer c-commands the head. This would violate the monotonicity requirement on c-command relations during the derivation, and we could therefore reduce the stipulation often used in TAG to a more general condition on monotonicity. Since complement auxiliary trees may not adjoin at a complement node, the obvious question is where they may adjoin. Clearly, adjoining at the root of a structure would not require any statements of c-command relations to be retracted, and thus is permissible. But

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Frank, Kulick and Vijay-Shanker

this is not an interesting situation as it can also be considered to be substitution. Saying that this derivation step is a case of adjoining is merely an artifact of the TAG formalism which, quite possibly, has no significant implications. The interesting cases correspond to adjoining complement auxiliary trees to internal nodes (i.e., non-root nodes). We adopt here Kayne’s (1994) suggestion that specifier positions should be assimilated to adjuncts, specifically with respect to their c-command relations (i.e., they c-command but are not c-commanded by their X 0 sister).8 This leads to the previously stated condition (10d), that a specifier c-commands the phrase to which it attaches. From this, we are able to derive the result that the only internal (non-root) nodes where complement auxiliary trees can adjoin are X 0 nodes that are sister to a specifier. The reason for this is exactly as in our discussion of the tree in Figure 11(a), namely that it is only in the context of unidirectional c-command from the specifier to the X0 node that it is possible to insert a complement auxiliary that will have the effect of lowering the X0 node. Interestingly, this view matches quite well what has been assumed in previous TAG analyses, where successive cyclic A0 -movement is accomplished by adjoining at C 0 as discussed earlier, and successive cyclic A-movement by adjoining at I0 . Indeed, we believe that this proposal provides a means of explaining why unbounded movement uniformly proceeds through specifier positions. We also derive contrasts in the use of modifier auxiliaries, as opposed to the complement auxiliaries. First, adjoining at the foot node of a modifier auxiliary will not be ruled out, as the modification relation does not entail mutual c-command, and such lowering of the foot does not force the retraction of any c-command relations. Second, since modifier auxiliary trees introduce an asymmetrical c-command relation with their foot node, it follows that their adjoining will not disrupt any c-command relations that the modified phrase already enters into. Thus, it follows the adjoining of modifier auxiliaries should be quite free and indeed may occur at any node in an elementary tree. In fact, if the root and foot of the auxiliary tree are considered segments of the same category (which explains the asymmetrical c-command relation between the modifier and modifiee), this would explain the possibility of multiple adjoining by modifier auxiliary trees at a single node considered by Shieber and Schabes.

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Monotonic C-Command: A New Perspective on TAG

(a)

(b)

IP



HH

DP Gabriel

H0 I

HH I to

C0

PP  P  P - IP C  I0

doesj

VP

HH

!!aa

V

DP

! - I 

eat

gnocchi

tj

a - VP "b " b  - I0 V

seem Figure 13. C-command-based elementary trees for raising with inversion

5.3. Returning to the Problematic Examples We suggest that our recasting of TAG derivations as manipulations of c-command relations leads to a resolution of the problems discussed in Section 3. Consider sentence (6), repeated here as (11): (11)

Does Gabriel seem to eat gnocchi?

The tree for the eat clause, given in Figure 6, is reinterpreted as a collection of c-command relations, shown in Figure 13(a), along the lines of the reinterpretation of tree Figure 4(a) as the one in Figure 11(a). 9 The c-command interpretation for the seem clause is shown in Figure 13(b). Recall that there was a relation between the two components in the tree set used for this derivation under the TL-MCTAG analysis, in Figure 9, in which the complementizer does had to substitute into the tree for eat at a “higher” position than where the seem tree adjoined in. However, that relationship could not be expressed by domination. Under our proposal, this relation is easily expressed in c-command terms, i.e., does must c-command seem. This c-command relation arises as the result of the movement of does from the I to C node, and does therefore needs to c-command its trace in I, as shown. We additionally represent the fact that the target of movement is a complementizer position by introducing the projection of the complementizer and its corresponding complementation relation into this elementary structure. Note that the absence of a specifier position means that this IP is essentially “floating” in the tree in Figure 13(b). The derivation proceeds by identifying the I 0 node of the structure in Figure 13(a) with the lower I0 node of Figure 13(b). It is still consistent with the original c-command relations for the auxiliary does to c-command Gabriel in its higher position. The structure in Figure 14 is therefore compatible with this derivation.

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Frank, Kulick and Vijay-Shanker 0

(Chhh h h - IP ((((hhhh - I0 DP ((((hhhh - VP Gabriel - I  (( (hhh ( h - I0 tj V  ```  - VP I seem PP V - DP to

((( ( C  doesj

eat gnocchi Figure 14. Result of c-command-based raising with inversion derivation

(a)

(b)

I

VP

H  H

HH  H

Clitic loi

I

PRO



V0

DP

IP

H  H

DPk

HH V mangiare

ti

Gabriel

H0 I

H  HH I

VP

vuolej

HH 0

tk

V

H  H V

VP

tj Figure 15. C-command-based elementary tree set and tree for clitic climbing

The tree set (10) for the clitic climbing case (9) is recharacterized in a similar way. As shown in (15), the clitic lo i c-commands its trace ti . We additionally represent the fact that the clitic must attach to an inflection node (see footnote 7) by showing the clitic as c-commanding the inflection node I. The tree (10) for the mangiare clause is reinterpreted as the ccommand relations in Figure 15(b). To derive (9), the VP node of Figure 15(a) is identified with the lower VP node of Figure 15(b). This allows the I node headed by lo to c-command the I node headed by vuole, resulting in the structure in Figure 16. 10 The extraposition example is handled in a very similar way, and we leave aside here the details.

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Monotonic C-Command: A New Perspective on TAG

17

IP





HH

HH

H0 I

DPk



Gabriel

HH

HH

I

VP

HH

H  H

Clitic loi

I vuolej

 tk

H0 V

H  HH V tj

VP



HH

PRO

H0 V

DP

HH V

ti

mangiare Figure 16. Result of clitic climbing derivation

6. The Structure of Derivations and Syntactic Locality The derivation of example (6) proceeds by identifying the I 0 node of Figure 13(a) with the lower I0 node of Figure 13(b). While such an operation is in part analogous to adjoining, it can also be considered as substitution of the “subtree”11 rooted by the I0 node in Figure 13(a) into the lower I0 node of Figure 13(b), with Gabriel “floating” up. We will take this version of substitution to be the basic operation of the derivation. When a derivation identifies two nodes, we call the node which is on the frontier of an elementary structure before the identification the substitution node.12 In general, applications of this substitution operation will not completely determine relative c-command relations among the pieces of the combined structures. In the particular derivation we have just seen, the substitution of one I0 into the other does not determine the relative ccommand relation of Gabriel and does. All we know is that both must c-command the I0 headed by the trace of does: the latter because of the c-command properties of movement and the former because the c-command relations of the I0 portion of Figure 13(b) are so tightly bound as not to allow floating within it. This means that either of Gabriel and does may c-command the other and still satisfy the ccommand relations determined through the combination of the two structures. Thus, the structure in Figure 14 is possible, but is not a necessary consequence. If we are to force the inversion of the auxiliary

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18

Frank, Kulick and Vijay-Shanker

I

H H  I to

VP

HH V

AP

H  H be

A

I

likely Figure 17. C-command-based infinitival raising auxiliary tree

around the subject, something further must be added. The intuition we are pursuing here is that a derivational analog of the CETM is in effect. Specifically, we believe that there is something illicit about the presence of two floating IP projections: one that includes the floating Gabriel and another that is the complement of the fronted does. The effect of the condition on the floating components is to force the identification of these two IP nodes, resulting in does c-commanding Gabriel and not conversely. For space reasons we leave aside here the precise characterization of the floating components, but we hope that the intuition is clear. Roughly put, then, our condition is as follows: (12)

Derivational CETM: After a substitution, the floating components of a derivation are resolved as part of exactly one extended projection.

For sentences with multiple levels of embedding, the range of derivational options increases. Consider, for example, the following example with two raising verbs: (13)

Does Gabriel seem to be likely to eat gnocchi?

We assume that the elementary structure headed by likely is as in Figure 17. There are a number of ways we might go about inserting the likely clause between the seem and to eat clauses while at the same time maintaining c-command relations during the course of the derivation. We could first combine the two raising predicates together to form a composite structure for seem to be likely and then combine this result with the eat clause. Alternatively, we could first combine the most embedded clause with the likely structure, adding the seem structure at the conclusion. We will permit only one of these derivations, ruling out the other via the following restriction: 13 (14)

The structure containing the substitution node must be elementary (that is, not the product of a derivation).

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Monotonic C-Command: A New Perspective on TAG

19

IP

  DP Gabriel

XXX

X X - I0 XX XX  - VP I  PP P  P - AP to V  PP P  P - I0 A  be PP  P  P

likely to eat gnocchi Figure 18. Intermediate result for c-command-based raising derivation

This condition can be seen as a natural addition to the Derivational CETM. In particular, it ensures that after each derivational step the structure above the substitution node (including the floating components of the substituted tree) will form a single extended projection. 14 Given the requirement in (14), the derivation must proceed “bottomup”, by substituting the I0 node of the Gabriel to eat gnocchi tree in Figure 13(a) into the I0 foot node of the to be likely tree in Figure 17. C-command monotonicity will guarantee that the result of this combination is as in Figure 18. The final step in the derivation substitutes the upper I 0 node from this structure into the foot I0 node of the structure for does...seem in Figure 13(b). Once again, c-command monotonicity coupled with the derivational CETM will result in the desired representation for (13), in this case that in Figure 19. Note that the alternative “top-down” derivation is ruled out by (14), since it would require the substitution of the I0 node of the Gabriel to eat gnocchi tree in Figure 13(a) into the foot node of the derived structure formed by the combination of the does. . . seem tree and the likely tree. 6.1. Maintaining Locality Constraints We believe that the derivational CETM as stated in (12), together with the condition on derivations given in (14), brings back into our system much of the restrictiveness of TAG in that it allows the combination of only simple structures or recursive combinations of them. Arbitrary structural combinations, along the lines allowed in DTG, are not permitted by the architecture of the formalism, and need not be ruled out by stipulated coherence constraints. It is a welcome result, therefore, that these derivational conditions also have the effect of ruling out certain cases of illicit long distance movement, such as super raising (as in (4), repeated here as (15)), without additional stipulation.

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20

Frank, Kulick and Vijay-Shanker

C0



H H 

HH

C

IP



doesj

HH

H0 I

DP



Gabriel

HH

I

H VP



tj

H  H

H0 I

V seem

H   HH I

VP

to

H  HH V

AP

be

H  HH I0

A likely



 P P

P

to eat gnocchi

Figure 19. Result of c-command-based multi-clausal raising with inversion

(a)

I0

"b " b I - VP "b " b  - IP V seems

(b)

IP

  DP it

PP

PP - I0 PPP  P - VP I  !aa !! a - AP isi V  "b " b A  - I0 ti

likely Figure 20. C-command-based elementary trees that cannot derive super raising

(15)

* Gabriel seems it is likely to eat gnocchi

Consider the structures in Figure 20, which might be used for such a derivation using our c-command approach, and which are in fact c-command reinterpretations of the TAG trees in Figure 5. These structures are different from those assigned earlier to seems and likely in a couple of crucial respects: the foot node of the seems tree is IP rather than I0 while the root node for the likely tree is IP as opposed to I0 , a result of the present of the expletive subject it. Because of the constraint from (14), this derivation must proceed by substituting the I0 node of a tree for Gabriel to eat gnocchi, i.e., Figure 13(a), into the I 0

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Monotonic C-Command: A New Perspective on TAG

21

IP

 DP Gabriel



H

HH

HH I0

DP it



HH

is

H VP

I



P PP  P 

P

likely to eat gnocchi

Figure 21. “Capture” of raised subject in c-command-based derivation

foot node of Figure 20(b), allowing Gabriel to “float up”. At this point in the derivation, there will be two distinct floating IP nodes with no c-command relations between them, one projected from the lower clause and one from the higher, each housing the subject of these two clauses. In this context, the derivational CETM will apply, forcing these two IP nodes to be identified, since otherwise these would constitute two distinct extended projections. The resulting structure will then be as in Figure 21. This identification of IPs does not yield any order or obligatory c-command relation between the two floating subjects it and Gabriel.15 However, the fact that there is no node “between” them that could substituted into some higher clause prevents Gabriel from being raised out of this clause, and indeed prevents the two subjects from being separated later on in the derivation. We assume that such a configuration with multiple specifiers of IP is ruled out, at least in English, for reasons that will depend on decisions, not relevant here, about representation of the analog of adjunction constraints in our system.16 One can imagine other ways of ruling out the super-raising case without recourse to our derivational constraints in (12) and (14). For example, one could simply stipulate that trees such as those in Figure 20 do not exist. Our very general derivational conditions have the advantage that, just as in the original TAG system, they also block other cases in which floating must be constrained, such as islands for extraction of wh-phrases and clitic climbing. 17 For example, without going into details, in a wh-island violation like that in (16), why will be unable to float up past the middle clause, as it will be stuck together with when in the intermediate [spec, CP] for reasons essentially identical to those in the super raising case. (16)

* Whyi do you wonder when John said [that Bill left t i ]?

Note that this is accomplished without any sort of resort to parochial constraints on floating nodes, as in DTG. We feel that this contrast

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Frank, Kulick and Vijay-Shanker

highlights a difference between our proposal and the DTG approach. DTG’s subsertion-insertion constraints in effect use the elementary structures in that system as a place to impose a global constraint on the final structure of the derivation. In contrast, our approach defines constraints on nodes present in the elementary structures, like in TAG and TL-MCTAG, and defines the composition operation in such a way that it, together with the locally defined constraints in the elementary structures, will derive the locality constraints. In that sense what we are doing is more like TAG and TL-MCTAG, as opposed to the DTG approach. 7. Conclusion We have discussed a reconceptualization of the elementary structures and corresponding derivations in TAG. By treating the fundamental relationship as one of c-command, we achieve the following results: 1. We have a better understanding of where the necessary dominance relations derive from in the systems of Rambow et al. (1995) and Vijay-Shanker (1992). 2. We explain a variety of constraints on the interaction of TAG elementary structures during adjoining or substitution. The same is true for related formalisms such as DTG, which need to stipulate why structures can only be substituted at certain places. 3. We resolve certain problematic cases for TAG, that had previously necessitated the use of TL-MCTAG or even more powerful systems 4. A pair of natural constraints on derivations, one a derivational analog of the CETM (12) and the other a translation of a TAG convention on adjoining (14), allows us to derive the effects of certain locality conditions on extraction.

Notes 1

If the tree sets have just one member, then it reduces to the case of basic TAG. One argument for this conclusion comes from contrasts involving VP fronting, in which a relative extraposed from the subject may not be moved, but one from the object must, indicating that the latter but not the former are within VP Baltin (1981)): 2

(i)

a.

Speak politely though people may who are from Boston, he still thinks they’re all a bunch of bums.

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Monotonic C-Command: A New Perspective on TAG

b. (ii)

a. b.

23

* Call people up though he may who are from Boston, he’s generally pretty cheap about long distance phone calls. * Speak politely who are from Boston though people may, he still thinks they’re a bunch of bums. Call people up who are from Boston though he may, he’s generally pretty cheap about long distance phone calls.

Anti-coreference contrasts point to a similar conclusion. As Kroch and Joshi note, object pronouns may corefer with names in a relative extraposed from subject position, as seen in (iiia). However, as seen in (iiib), if the relative is extraposed from object position, such coreference is impossible. (iii)

a. b.

Many people visited heri who cheered Maryi up. * I told many people about heri who were interested in Maryi .

We take this to indicate that the landing site for object but not subject extraposition is c-commanded by the object, and hence within VP. 3 The system we propose also requires a constraint on derivations to rule out undesired cases such as the super-raising violation. In section 6 we discuss the different characteristics of our approach and that of DTG. 4 Frank (1992) suggests instead that there should be a c-command link between the members of the tree set in Figure 9. Quite clearly, this is in the spirit of the current proposal. 5 If the analysis of (6) were reworked so that both specifiers and heads in the multi-component set adjoin in, it would be possible to specify the links between the components as domination links. For example, if all the nodes above VP were simply further projections of VP with appropriate features added, then the trees in Figure 9 could be rewritten as follows (with corresponding changes in the tree for Gabriel to eat gnocchi). (i)

a.

b.

VP

H  H V does

VP

VP

H  H V

VP

seem

Here a domination link could be specified between the foot VP node of (ia) and the root VP node of (ib). So while it is not impossible to use the domination relation to characterize a multi-component tree set to derive this particular case, maintaining the restriction to a domination relation forces a linguistic analysis which we take to be undesirable. Given that there are other cases in which the domination relation becomes increasingly cumbersome, e.g., clitic climbing, we conclude that TAG extensions resting on the use of domination relationships are inappropriate for linguistic analysis. 6 The trees in this example are based on an analysis in which the clitic attaches to the inflection node, and clitic climbing occurs when the lower clause is “defective”, projecting only to VP, thus forcing the clitic to climb. Even if a different analysis is used, as long as the assumption is made that the clitic attaches to the same node as the matrix verb, domination will be insufficient to express the relation between the two halves of the elementary tree. 7 The lines indicating direct domination in Figure 11(a) are not intended as part of the representation, but rather as aid to the reader in comparing our proposed

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Frank, Kulick and Vijay-Shanker

structure to that standardly assumed. Note that certain implicit c-command relations, such as that between C and the subconstituents of IP are suppressed in this figure, but we assume that they are present. See Frank and Vijay-Shanker (1998a) for extensive discussion of the properties of structures defined in terms of c-command and the relationship between such structures and those defined in terms of dominance. 8 This raises the interesting possibility that specifiers could be adjoined in the TAG sense as well. Although this would have certain benefits with respect to the treatment of subject islands, we believe at present that it is not immediately compatible with our proposal to derive the possible loci of adjoining from c-command monotonicity. 9 One difference between the two cases is that the complementizer is not included in the structure in Figure 13(a). While we are still investigating the exact conditions under which it should be included as part of the elementary structure, one promising hypothesis is that it need not be included when the clause is headed by the defective inflectional head present in raising complements. 10 We have left out some of the c-command relations in Figures 15 and 16 to avoid clutter. Also, note the c-command relation in Figure 16 between the I node headed by loi and its trace ti . This is an instance in which the tree representation of the c-command relations is a bit misleading, since the I node headed by loi appears to c-command the I node headed by vuolej , but nothing else. However, loi is simply adding an asymmetrical c-command relation to the I node headed by vuolej , and so the I node headed by loi c-commands everything that the node headed by vuolej c-commands, including the trace ti . 11 Technically, a subset of the c-command relations of Figure 13(a). 12 Analogs to the constraints on adjoining discussed in Section 5 are still derived when substitution is taken to be the basic operation. 13 Note that (13) is not derivable within TL-MCTAG, even ignoring the dominance problem mentioned earlier. Assuming that the derivation proceeds by the seem tree (set) adjoining to the root of the likely tree, with the result adjoining into the eat tree, a locality problem will arise. If does and seem are a multi-component tree set, then does needs to substitute into the eat tree while seems adjoins into the likely tree, thus violating tree-locality. Kulick (1998) notes that this problem can be avoided by allowing adjoining at a foot node, therefore allowing to be likely to adjoin at the foot node of the seem tree. While the full implications of this approach are not yet fully understood, such adjoining at a foot has traditionally been prohibited in TAG. Indeed, as discussed in Section 5, the recharacterization of TAG derivation argued for in this paper in fact rules out adjoining a complement auxiliary tree at the foot node of a complement auxiliary tree. 14 Alternatively, one could reformulate the Derivational CETM along the following lines: (i)

Derivational CETM: After a substitution, the structure above the site of substitution must be resolved as part of exactly one extended projection.

Apart from reproducing the effects of the formulation of the derivational CETM in (12), this version would have the additional consequence of allowing the elimination of condition (14). 15 The relative ordering depicted in Figure 21 is thus only one of two possibilities. Both will, however, suffer the same fate.

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Monotonic C-Command: A New Perspective on TAG

25

16

Possibilities include a violation of the extended projection principle or lack of Case for Gabriel and/or it. 17 The advantage of blocking locality violations by these general derivational conditions also extends to more complicated cases of multiple clitic climbing within one sentence. See Kulick et al. (1999) for a detailed discussion of these cases within the context of the system discussed here.

Acknowledgments We are grateful to three anonymous reviewers for their helpful comments, as well as to the National Science Foundation for their financial support of this work in the form of grants SBR-97-10247, SBR-8920230, and SBR-97-10411 for the three authors respectively. References Baltin, M.: 1981, ‘Strict Bounding’. In: C. L. Baker and J. J. McCarthy (eds.): The Logical Problem of Language Acquisition. Cambridge, MA: MIT Press, pp. 257–295. Becker, T., A. K. Joshi, and O. Rambow: 1991, ‘Long-Distance Scrambling and Tree Adjoining Grammars’. In: Proceedings of the Fifth Conference of the European Association for Computational Linguistics. Berlin. Bleam, T.: 1994, ‘Clitic Climbing and the Power of Tree Adjoining Grammar’. Manuscript, University of Delaware. Frank, R.: 1992, ‘Syntactic Locality and Tree Adjoining Grammar: Grammatical, Acquisition and Processing Perspectives’. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA. Frank, R. and K. Vijay-Shanker: 1998a, ‘Primitive C-Command’. Manuscript, Johns Hopkins University and University of Delaware. Frank, R. and K. Vijay-Shanker: 1998b, ‘TAG Derivation as Monotonic CCommand’. In: Proceedings of the Fourth International Workshop on Tree Adjoining Grammars and Related Formalisms. University of Pennsylvania, pp. 46–49. Grimshaw, J.: 1991, ‘Extended Projection’. Manuscript, Brandeis University. Harley, H. and S. Kulick: 1998, ‘TAG and Raising in VSO Languages’. In: Processdings of the Fourth International Workshop on Tree Adjoining Grammars and Related Frameworks (TAG+4). IRCS Report 98–12. Kayne, R.: 1994, The Antisymmetry of Syntax. Cambridge, MA: MIT Press. Kroch, A.: 1987, ‘Unbounded Dependencies and Subjacency in a Tree Adjoining Grammar’. In: A. Manaster-Ramer (ed.): The Mathematics of Language. Amsterdam: John Benjamins, pp. 143–172. Kroch, A.: 1989, ‘Asymmetries in Long Distance Extraction in a Tree Adjoining Grammar’. In: M. Baltin and A. Kroch (eds.): Alternative Conceptions of Phrase Structure. Chicago, IL: University of Chicago Press, pp. 66–98. Kroch, A. and A. K. Joshi: 1985, ‘The Linguistic Relevance of Tree Adjoining Grammar’. Technical Report MS-CS-85-16, Department of Computer and Information Sciences, University of Pennsylvania.

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Kroch, A. and A. K. Joshi: 1987, ‘Analyzing Extraposition in a Tree Adjoining Grammar’. In: G. Huck and A. Ojeda (eds.): Discontinuous Constituents, Vol. 20 of Syntax and Semantics. New York: Academic Press, pp. 107–149. Kulick, S.: 1997, ‘Generalized Transformations and Restructuring in Romance’. In: Proceedings of the 14th Eastern States Conference on Linguistics. Kulick, S.: 1998, ‘Constrained Non-Locality in Syntax: Long-Distance Dependencies in Tree Adjoining Grammar’. Dissertation Proposal, University of Pennsylvania. Kulick, S., R. Frank, and K. Vijay-Shanker: 1999, ‘Defective Complements in Tree Adjoining Grammar’. In: Penn Working Papers in Linguistics. Univerisity of Pennsylvania, Department of Linguistics. Rambow, O.: 1994, ‘Formal and Computational Aspects of Natural Language Syntax’. Ph.D. thesis, University of Pennsylvania, Philadelphia, PA. Rambow, O., K. Vijay-Shanker, and D. Weir: 1995, ‘D-Tree Grammars’. In: Proceedings of the 33rd Annual meeting of the Association for Computational Linguistics. Cambridge, MA, pp. 151–158. Schabes, Y. and S. Shieber: 1994, ‘An Alternative Conception of Tree Adjoining Derivation’. Computational Linguistics 20, 91–124. Vijay-Shanker, K.: 1992, ‘Using Descriptions of Trees in a Tree Adjoining Grammar’. Computational Linguistics 18, 481–518.

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